Assessment of the double-parameter iterative Tikhonov regularization for single-epoch measurement model-based precise GNSS positioning

Abstract

The double-parameter iterative Tikhonov regularization is assessed for strengthening the single-epoch model-based precise GNSS positioning within the framework of cognitive meanings. The simultaneous iterative Tikhonov regularization of the least-squares (LS) estimators of the parameters of interest in the single-epoch GNSS model is analyzed to enhance their accuracy properties. Regularization parameters (RP) are collected in the regularization operator, which can play a standardizing role in the regularization principle. Thus, the double-parameter approach can consider the heteroscedasticity of the LS estimators of interest in the regularization principle. This approach employs the quality-based mean squared error (mse) matrix trace minimization criterion to select optimal double-RP values simultaneously. Then, the unconstrained LS estimation is iteratively regularized, obtaining regularized float solutions. The numerical tests indicate that the double-parameter approach successfully strengthens the single-epoch GNSS measurement models due to considering the heteroscedasticity of the LS estimators of interest in the regularization principle. The regularized variance–covariance (vc) matrix describes float solutions of improved precision properties at the cost of losing the LS estimator’s unbiasedness. The accuracy is thus superior in the sense of mse. Therefore, the regularized LS estimator is well-scaled but with a biased localization. It also provides a more peaked probability density function (PDF) of real-valued ambiguities, obtaining a lower failure rate (FR) of integer least-squares (ILS) ambiguity resolution (AR). In this way, the regularized ILS estimator performs well in the ambiguity domain with the presence of regularized bias.